988
Index
Open domain, 400
Open set, 392
Operator, 172, 387, 404
Operator equation, 404
Operator preserving norm
Operator with dense domain, 409
Optimal price policy problem, 122
Optimal shape of a sewing machine needlepoint, 130
Ordered pair, 386
Orthogonal, 401
Orthogonal system, 401
Ostrogradsky equation, 159
Ostrogradsky formula, 24
Outer multiplication, 63
Outer product, 63
P
Parallelogram formula, 399
Parameter, 4
Parseval equality, 403
Partial differential operator, 172
Partial sum, 402
Particle, 514
Particle system, 514
Perfect set, 392
Permutation operator, 53
Permutation symbol, 54
Permutation tensor, 53
Phase space, 386
Piecewise continuously differentiable path,
295
Piecewise extremal curve, 297
Piola stress tensor, 696
Planck(’s) constant, 634
Plateau(’s) problem, 92, 639
Poincaré inequality, 443
Point, 384, 389
Point function, 8
Point of accumulation, 391
Point set, 385
Poisson(’s) equation, 167, 628, 729
Polarization identity, 400
Polygonal line, 295
Position constraint, 515
Positive definite function, 519
Positive definiteness, 389, 393, 394
Positive definite operator, 411
Positively homogeneous function of order n,
366
Positively n-th order homogeneous function,
366
Positive operator, 411
Possible displacement, 530
Possible strain, 530
Possible stress, 530
Potential energy, 522
Potential energy density, 550
Potential energy function, 550
Potential energy of external force, 537
Potential field, 15, 522
Potential force, 522
Potential function, 15, 549
Potential operator, 412
Power set, 386
Poynting equation, 633
Poynting(’s) vector, 633
Poynting theorem, 633
Preimage, 387
Principal value, 65
Principle of complementary virtual work,
543
Principle of duality, 343
Principle of generalized virtual displacement, 531
Principle of generalized virtual work, 531
Principle of least action, 549
Principle of mechanics, 513
Principle of minimum complementary
energy, 545
Principle of minimum potential energy, 478,
536
Principle of possible work, 531
Principle of reciprocity, 343
Principle of stable action, 549
Principle of total complementary energy,
545
Principle of virtual displacement, 479, 526
Principle of virtual stress, 543
Principle of virtual work, 526
Problem for determining solution, 96
Problem of brachistochrone, 86
Problem of compressive bar stability, 524
Problem of curve of steepest descent, 86
Problem of least (or minimal) surface of
revolution, 137
Produce set, 387
Product set, 387
Projection, 387
Proper field, 201
Proper path, 516
Proper subset, 386
p-th power summable sequence space, 393
Index
Open domain, 400
Open set, 392
Operator, 172, 387, 404
Operator equation, 404
Operator preserving norm
Operator with dense domain, 409
Optimal price policy problem, 122
Optimal shape of a sewing machine needlepoint, 130
Ordered pair, 386
Orthogonal, 401
Orthogonal system, 401
Ostrogradsky equation, 159
Ostrogradsky formula, 24
Outer multiplication, 63
Outer product, 63
P
Parallelogram formula, 399
Parameter, 4
Parseval equality, 403
Partial differential operator, 172
Partial sum, 402
Particle, 514
Particle system, 514
Perfect set, 392
Permutation operator, 53
Permutation symbol, 54
Permutation tensor, 53
Phase space, 386
Piecewise continuously differentiable path,
295
Piecewise extremal curve, 297
Piola stress tensor, 696
Planck(’s) constant, 634
Plateau(’s) problem, 92, 639
Poincaré inequality, 443
Point, 384, 389
Point function, 8
Point of accumulation, 391
Point set, 385
Poisson(’s) equation, 167, 628, 729
Polarization identity, 400
Polygonal line, 295
Position constraint, 515
Positive definite function, 519
Positive definiteness, 389, 393, 394
Positive definite operator, 411
Positively homogeneous function of order n,
366
Positively n-th order homogeneous function,
366
Positive operator, 411
Possible displacement, 530
Possible strain, 530
Possible stress, 530
Potential energy, 522
Potential energy density, 550
Potential energy function, 550
Potential energy of external force, 537
Potential field, 15, 522
Potential force, 522
Potential function, 15, 549
Potential operator, 412
Power set, 386
Poynting equation, 633
Poynting(’s) vector, 633
Poynting theorem, 633
Preimage, 387
Principal value, 65
Principle of complementary virtual work,
543
Principle of duality, 343
Principle of generalized virtual displacement, 531
Principle of generalized virtual work, 531
Principle of least action, 549
Principle of mechanics, 513
Principle of minimum complementary
energy, 545
Principle of minimum potential energy, 478,
536
Principle of possible work, 531
Principle of reciprocity, 343
Principle of stable action, 549
Principle of total complementary energy,
545
Principle of virtual displacement, 479, 526
Principle of virtual stress, 543
Principle of virtual work, 526
Problem for determining solution, 96
Problem of brachistochrone, 86
Problem of compressive bar stability, 524
Problem of curve of steepest descent, 86
Problem of least (or minimal) surface of
revolution, 137
Produce set, 387
Product set, 387
Projection, 387
Proper field, 201
Proper path, 516
Proper subset, 386
p-th power summable sequence space, 393